Space inversion and other discrete symmetries are treated within the frame of a theory of fundamental forces based only on general considerations of causality, symmetry, and stability, without ad hoc differential equations. The basic space-time ˜M is the Einstein universe R1 × S3 as a causal (or conformal) rather than a pseudo-Riemannian manifold. Its connected symmetry group is then a 15-parameter group ˜G locally equivalent to SO(2, 4), while the isometry group ˜K of the Einstein universe is a 7-parameter subgroup. Correlation with conventional relativistic theory is based on a canonical imbedding of Minkowski space M0 into ˜M, together with the unique extendability of all transformations of the scaling-extended Poincaré group ˜P from M0 to global transformations on ˜M. The fundamental fermion field F and boson field B are here restricted to be real and are fully invariant under ˜Ge, where the superscript e denotes the inclusion of space and time inversions. The role of C on F is taken over by a real matrix having the eigenvalues ±i, that commutes with ˜G but anticommutes with space inversion. The spin space for B consists of the real linear transformations on that for F. There is a corresponding natural total Lagrangian that is both ˜Ge and O(2)-gauge invariant, the latter leading to lepton and baryon number conservation, and which is nonparametric except for scale. The Weyl and Maxwell equations are deduced, and compelling identifications made for neutrinos and the photon. The e and μ neutrino pairs occur in strikingly inequivalent positions in F, appearing symmetric only in the conventional relativistic limit R → ∞, where R is the (˜G-invariant) fundamental length interpretable as the radius of the space S3. The photon occurs as the lowest member of a coherent subfamily of B that includes natural candidates for bare versions of the W and Z particles. In the relativistic limit the interaction Lagrangian becomes a sum over all elementary processes, one of which appears as quantum electrodynamics with Majorana-type electrons.
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机译：在基本力理论的框架内，仅基于因果关系，对称性和稳定性的一般考虑，而无需特殊的微分方程，即可处理空间反演和其他离散对称性。基本时空M是爱因斯坦宇宙R 1 ×S 3 作为因果（或共形）而不是伪黎曼流形。然后，它的连接对称组是局部等于SO（2，4）的15参数组〜G，而爱因斯坦宇宙的等距组〜K是7参数子组。与传统相对论的相关性基于Minkowski空间M0到〜M的规范嵌入，以及缩放扩展的Poincaré组〜P从M0到〜M的全局变换的所有转换的唯一可扩展性。这里的基本费米子场F和玻色子场B被限制为实数，并且在〜G e 下完全不变，其中上标e表示包含空间和时间倒置。 C在F上的作用由具有特征值±i的实矩阵取代，该特征值与〜G交换但与空间求逆反交换。 B的自旋空间由F的实线性变换组成。存在一个相应的自然总拉格朗日数，它既是〜G e 也是O（2）规不变，后者导致轻子以及重子数守恒，并且除了规模外都是非参数的。推导了Weyl和Maxwell方程，并对中微子和光子进行了令人信服的鉴定。 e和μ中微子对出现在F的显着不等位置，仅在常规相对论极限R→∞中对称，其中R是（〜G不变）基本长度，可解释为空间S 3的半径。光子作为B相干子家族的最低成员出现，该子家族包括W和Z粒子裸露版本的自然候选者。在相对论极限中，拉格朗日相互作用成为所有基本过程的总和，其中之一表现为马约拉那型电子的量子电动力学。
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